Abstract Radio waves propagating through a medium containing irregularities in the spatial distribution of the electron density develop fluctuations in their intensities and phases. In the case of radio waves emitted from astronomical objects, they propagate through electron density irregularities in the interstellar medium, the interplanetary medium, and Earth’s ionosphere. The LOFAR radio telescope, with stations across Europe, can measure intensity across the VHF radio band and thus intensity scintillation on the signals received from compact astronomical objects. Modeling intensity scintillation allows the estimate of various parameters of the propagation medium, for example, its drift velocity and its turbulent power spectrum. However, these estimates are based on the assumptions of ergodicity of the observed intensity fluctuations and, typically, of weak scattering. A case study of single-station LOFAR observations of the strong astronomical source Cassiopeia A in the VHF range is utilized to illustrate deviations from ergodicity, as well as the presence of both weak and strong scattering. Here it is demonstrated how these aspects can lead to misleading estimates of the propagation medium properties, for example, in the solar wind. This analysis provides a method to model errors in these estimates, which can be used in the characterization of both the interplanetary medium and Earth’s ionosphere. Although the discussion is limited to the case of the interplanetary medium and Earth’s ionosphere, its ideas are also applicable to the case of the interstellar medium.